WHOLE LOTTA TROUBLE: Lions quarterback Shaun Hill eludes Patriots linebacker Rob Ninkovich last week in Detroit. The Pats won 45-24 — and are 9-2 in spite of a defense ranked next-to-last in the NFL. Photo: AP

FOXBOROUGH, Mass. — No. 12 has been terrific, but 31 could be a much more telling number for the Patriots than 9-2.

Alleged defensive genius Bill Belichick’s group is 31st in the NFL in total defense and trending downward as New England heads into Monday night’s AFC East showdown with the Jets here. Only the Redskins are worse.

That shockingly terrible statistic — not to mention the Patriots’ last-place ranking in pass defense — hasn’t been enough so far to get in the way of Tom Brady’s greatness or prevent nine wins in their first 11 games.

But rare is the team that advances far in the postseason with one of the worst defenses in the league, and the Patriots know it.

“We’re 9-2, but we’re not satisfied with our ranking on defense or our stats or numbers on that side of the ball,” second-year cornerback Kyle Arrington said yesterday. “It’s not like we’re not working on it.”

Arrington, a Hofstra product, realizes a youth-laden Patriots defense that starts three rookies still has much to fix for New England to even think about winning its fourth Super Bowl this century.

None of the first three Patriot teams to win a Lombardi Trophy was worse than 19th in the league in total defense, but this year’s group isn’t even within shouting distance of that low-water mark set by the 2001 edition.

Not only is Belichick’s team giving up 399.1 yards a game to rank 31st in total defense (down one spot from last week after a 45-24 win over the woeful Lions) and sitting 32nd in pass defense, but the Patriots are just 16th in run defense and 22nd in scoring D.

New England has been able to string together a tie for the AFC’s best record mostly because another super Brady season has resulted in the Patriots leading the NFL in scoring at 30.4 points a game.

But is that any way to win a championship? Logic would appear to say “no,” but Arrington and has defensive mates aren’t hiding their heads in shame.

“You could say we’ve had a bend-but-don’t-break mentality [on defense] this year,” Arrington said. “We’ve given up some stuff, but we’ve also made a lot of plays on defense. We’ve made plays when we needed to make plays.”

That’s true, considering the Patriots are among the NFL’s leaders with a plus-11 turnover margin thanks in large part to five interceptions by cornerback Devin McCourty that have the put the Rutgers second-round pick in contention for Rookie of the Year honors.

The turnovers have often been timely, too, with the most recent example coming in a Week 11 home win over the Colts, when safety James Sanders intercepted Peyton Manning at the New England 6 with just 31 seconds left to preserve a 31-28 win.

But a team can walk the high wire on defense for only so long in the NFL, particularly if it’s counting on the quarterback to win a shootout every week and especially once the playoffs start and points are often hard to come by.

So far, Brady has been able to mask a defense that has allowed at least 18 points in all but one game (a 41-14 win at Miami in Week 4) and has been riddled the past four contests by the likes of Cleveland and Detroit.

The “Ride Brady” strategy might work again Monday, but the Patriots don’t need to be reminded that a victory over the Jets this time around could be a case of winning the battle but not the war unless their defense suddenly gels.

“We’re well aware that we’ve got to start living up to our end of the bargain as a defense,” Arrington said. “The good thing is that we’re 9-2, and there’s still time left in this season. That’s something to build on.”